Learn the basic concepts of measurement and uncertainty, also within a statistical approach. Critically apply those concepts to the acquisition, analysis and interpretation of experimental data, with particular emphasis on electrical and electronic quantities. Learn basic knowledge on electrical and electronic instruments, and on their use in the laboratory.
teacher profile | teaching materials


• Introduction to metrology: basic definitions;
• Systems of measurement units (international system of measurement units, CGS systems, Gaussian system): definitions, writing rules and conversion methods;
• Elements of inferential statistics: histograms, position parameters, dispersion parameters, shape parameters, empirical law of frequency, law of large numbers, central limit theorem;
• Evaluation of uncertainty in direct measurements: basic definitions, type A and type B uncertainty, sample mean and variance and their distributions, notable distributions (Gaussian, uniform, t-student), expanded uncertainty;
• Statistical tests: chi-square test, mean test;
• Evaluation of uncertainty in indirect measurements: uncertainty propagation rule in indirect measurements (JCM 100:2008), deterministic model of uncertainty and propagation rule in indirect measurements (maximum error).
• Graphing and mathematical methods: graphing, bi/semi-logarithmic graphs, fit procedures, least squares method.
• Real passive components: resistors, capacitors, inductors;
• Analog measuring instruments: static/dynamic metrological characteristics, D'Arsonval ammeter, electrostatic voltmeter, electrodynamic instrument, analog wattmeter, dc insertion errors of voltmeters and ammeters.
• Electrical resistance measurement methods: voltamperometric method, 2/4-point measurements, DC measurement bridges – Wheatstone bridge, van der Pauw method for resistivity measurement.
• Digital measuring instruments: AD converters, digital voltmeters;
• The oscilloscope: analog oscilloscope, digital oscilloscope, sampling methods, aliasing;
• Electrical noise (outline): sources and types of noise, noise reduction techniques.

Core Documentation

International vocabulary of metrology – Basic and general concepts and associated terms (VIM – 3rd ed.)
Evaluation of measurement data — Guide to the expression of uncertainty in measurement
The International System of Units – 9th edition – brochure

Reference Bibliography

Selected chapters from: R. Bartiromo, M. De Vincenzi “Electrical Measurements in the Laboratory Practice”, Springer P. Fornasini “The Uncertainty in Physical Measurements”, Springer J. R. Taylor, “An Introduction to Error Analysis”, 2nd ed., University Science Book W. Navidi, “Statistics for Engineers and Scientists”, 3rd ed., McGraw-Hill I. G. Hughes, T. P. A. Hase “Measurements and their Uncertainties”, Oxford University Press, 2010 R. B. Northrop “Introduction to Instrumentation and Measurements”, CRC Press A. Carullo, U. Pisani, A. Vallan, “Fondamenti di misure e strumentazione elettronica”, CLUT editrice 2020 A.K. Sawhney, “A course in electrical and electronic measurements and instrumentation”, Dhanpat Rai & co, 19th ed

Type of delivery of the course

In presence with lectures, classroom and laboratory exercises


optional participation

Type of evaluation

On-the-go mode: A – Written test on the first part of the course B - Evaluation of Laboratory Reports C - Final oral The final grade is the average of the three tests Or full exam: - Extended written test (valid only for the exam session) - Oral, also on the part relating to the laboratory